Presently, ten speed bicycle transmissions consist of a chain wrapped around a front double sprocket and a rear cluster containing five sprockets, a front derailleur and a rear derailleur for derailing the chain from one sprocket to another in response to a rider moving two control levers which are connected to the derailleurs. The derailleurs are made of a large number of delicate parts which need frequent maintenance and are easily damaged. The derailleur system is also hard to operate, it generates a continuous noise and inefficiencies in certain gears due to chain's misalignment and it calls for a frequent visual inspection by the rider, to visually verify the gear ratio he is in, diverting his attention from the road. For these reasons several attempts have been made in the past to introduce different systems, some of which are based on variable sprockets. Examples of such efforts can be found in U.S. Pat. Nos. 3,850,044 and 3,850,045. Some of the reasons for such systems being commercially unsuccessful, on a large scale, were their complexity, high cost, added weight and maintenance problems. Another example is found in British Pat. No. 453712 where the two flanges are stacked together with the planets being side saddled in a cantilevered position. Such an arrangement induces severe stresses under working loads which leads to severe deformation of the variable sprocket under working loads, especially since the flanges have to be perforated and loose most of their structural integrity. These deformations interfere with the synchronization of the sprocket-segment-planets and the chain. In contrast, the object of the present invention is to overcome these and other problems, and provide a simple durable system which can be economically mass produced from metal or molded plastic.